Creamer, an 18-year-old American rookie, shot a 66 to stand at 14-under 202 and seven ahead of the twice winner Davies, who hit a 70, and France's own Karine Icher, who surged through the field with a 68.
"Paula's going to be hard to beat but it's the sort of course where you can hit low numbers and it will be good fun trying to catch her," said Davies, who was champion at the Evian Masters in 1995 and 1996.
"And if I don't, it should be good fun watching her."
Creamer, who won the Sybase Classic in New York in May, had seven birdies and holed five putts of 15 feet or more.
She has had three top-five finishes in a run of five tournaments, but her pursuers have been given a glimmer of hope by the fact that she led by five shots with seven holes to play in the final round of the Rochester Classic last month, but was still overtaken by the Mexican player Lorena Ochoa.
The world No 1, Annika Sorenstam, played with Creamer, but could only manage a 72 and slipped into fourth place, eight shots behind.
"Paula played great and I didn't," she said of a round which included a double-bogey six at the 12th. "I think I'll need a 64 at least to have a chance."
Michelle Wie, the 15-year-old American amateur, moved into the top 10 on three under par after a fine 68 made up of seven birdies and in spite of a triple-bogey seven at the fourth, where she took five shots to get down from the back of the green. It was her best round in two visits to Evian.
"It started out good, got really bad, then really good and then OK," Wie said afterwards.
"It was like all four seasons in one day."Reuse content